Certificate for #7280 ⟨a, b, c | ab=1, aaaa=cb⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(c) = deg(b) = 0, c < b; deg(a) = 1

Axiom: ab=1.

Referenced by [3], [5], [7], [9], [11].

Axiom: aaaa=cb.

Referenced by [3], [4], [6].

Overlap of [2] aaaa=cb with [1] ab=1:

Critical pair: aaa=cbb.

Referenced by [6], [7], [8].

Overlap of [2] aaaa=cb with [2] aaaa=cb:

Critical pair: acb=cba.

Flip LHS and RHS.

Referenced by [5].

Overlap of [4] cba=acb with [1] ab=1:

Critical pair: cb=acbb.

Flip LHS and RHS.

Referenced by [6], [8], [10].

Overlap of [2] aaaa=cb with [5] acbb=cb:

Critical pair: aaacb=cbcbb.

Reduce LHS:

Defines rule #1.

Referenced by [8].

Overlap of [3] aaa=cbb with [1] ab=1:

Critical pair: aa=cbbb.

Referenced by [8], [9], [10].

Overlap of [3] aaa=cbb with [5] acbb=cb:

Critical pair: aacb=cbbcbb.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [10].

Overlap of [7] aa=cbbb with [1] ab=1:

Critical pair: a=cbbbb.

Defines rule #5.

Referenced by [10], [11].

Overlap of [7] aa=cbbb with [5] acbb=cb:

Critical pair: acb=cbbbcbb.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Overlap of [1] ab=1 with [9] a=cbbbb:

Critical pair: cbbbbb=1.

Defines rule #3.